基于LSSVM算法的模糊建模及在铸造设备控制中的应用
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摘要
模糊辨识就是采用模糊集合理论，根据系统的输入输出值来辨识系统的模糊模型。目前，它被广泛地应用于非线性系统的辨识中。现有辨识算法仍存在一些难题，例如避免“维数灾难”和提高模型泛化能力的问题。模糊模型辨识主要分为结构辨识和参数辨识两个部分，其中最重要的便是结构辨识，目前尚未形成对结构辨识完善的理论。而且，目前的一些模糊模型辨识方法很难应用到实际生产过程中，其中一个主要的原因就是传统辨识方法存在计算复杂度高与庞大的规则库的问题。因此，本文研究的主要出发点就是如何设计简单有效的辨识算法，以及减少其计算复杂度，使其适用于工业生产过程中。
本文研究了一种基于最小二乘支持向量机（LSSVM）的T-S模糊建模新方法，提出了一种基于LSSVM的模糊内模控制策略，然后将其应用到先进铸造设备的定量浇铸控制。主要做了以下工作：
（1）针对标准支持向量机模糊建模方法的计算复杂度高问题，引入LSSVM算法的等式约束，明显的提高了建模效率。
（2）通过LSSVM算法对模糊模型进行结构划分，实现模糊模型的结构辨识；在不改变训练参数的情况下，通过剪枝算法得到具有稀疏性的支持向量，依据支持向量的个数来划分模糊空间，从而使得模型结构简单，便于应用推广。
（3）将LSSVM模糊模型引入内模控制中，将其作为系统的内部模型，并且根据该模型设计了逆模型控制器。
（4）设计了整个定量浇铸控制系统。主要分析了定量浇铸加压控制系统的控制特点，建立了仿真模型。仿真结果表明，在定量浇铸的液面加压系统中，基于LSSVM的模糊模型的内模控制方法在控制精度上和抗干扰能力方面都具有一定的优越性。
Fuzzy Identification is to identify the fuzzy model of the system from the measured values of system inputs and outputs, using fuzzy set theory, it has a very wide range of applications in the field of nonlinear system identification. However, the existing identification algorithm is still facing the problems of how to avoid the curse of dimensionality and improve the model generalization capability. Fuzzy Model Identification includes structure identification and parameter identification. One of the most important is the structure identification, and it has not formed a theory on the structure identification. Moreover, there are still many difficulties in the application of fuzzy model identification in actual industrial processes. One of reasons is the huge rule base generated by the traditional identification methods, and consumption of identification calculation. Therefore, the main purpose of this paper is how to design a simple and effective identification algorithm, how to reduce the identification algorithm computing complexity.
In this paper, we do some research on TS fuzzy modeling based on least squares support vector machine (LSSVM), and proposed a method of LSSVM-based fuzzy model control. Then we applied it in advanced casting equipment constant casting control system and mainly done the following work:
1) For the high computational complexity problem in fuzzy modeling method based on standard support vector machine, the introduction of the LSSVM with equation constraints, significantly improved the efficiency of modeling.
2) The structure of fuzzy model is identified using the LSSVM algorithm; the sparse support vectors are gotten through the pruning algorithm without changing the training parameters; the Fuzzy space is divided based on the number of support vectors. It simplifies the structure of the fuzzy model, and promotes its application.
3) The LSSVM fuzzy model is introduced into the internal model control, and used as the system's internal model. The inverse model controller is designed according to this modeling method.
4) A constant casting control system is designed. A simulation model is built after the analysis of features of the constant casting pressure control system. The simulation results show that quantitative casting surface pressure systems, internal model control method based on of LSSVM fuzzy model has certain advantages in the control precision and anti-interference capability.
本文研究了一种基于最小二乘支持向量机（LSSVM）的T-S模糊建模新方法，提出了一种基于LSSVM的模糊内模控制策略，然后将其应用到先进铸造设备的定量浇铸控制。主要做了以下工作：
（1）针对标准支持向量机模糊建模方法的计算复杂度高问题，引入LSSVM算法的等式约束，明显的提高了建模效率。
（2）通过LSSVM算法对模糊模型进行结构划分，实现模糊模型的结构辨识；在不改变训练参数的情况下，通过剪枝算法得到具有稀疏性的支持向量，依据支持向量的个数来划分模糊空间，从而使得模型结构简单，便于应用推广。
（3）将LSSVM模糊模型引入内模控制中，将其作为系统的内部模型，并且根据该模型设计了逆模型控制器。
（4）设计了整个定量浇铸控制系统。主要分析了定量浇铸加压控制系统的控制特点，建立了仿真模型。仿真结果表明，在定量浇铸的液面加压系统中，基于LSSVM的模糊模型的内模控制方法在控制精度上和抗干扰能力方面都具有一定的优越性。
Fuzzy Identification is to identify the fuzzy model of the system from the measured values of system inputs and outputs, using fuzzy set theory, it has a very wide range of applications in the field of nonlinear system identification. However, the existing identification algorithm is still facing the problems of how to avoid the curse of dimensionality and improve the model generalization capability. Fuzzy Model Identification includes structure identification and parameter identification. One of the most important is the structure identification, and it has not formed a theory on the structure identification. Moreover, there are still many difficulties in the application of fuzzy model identification in actual industrial processes. One of reasons is the huge rule base generated by the traditional identification methods, and consumption of identification calculation. Therefore, the main purpose of this paper is how to design a simple and effective identification algorithm, how to reduce the identification algorithm computing complexity.
In this paper, we do some research on TS fuzzy modeling based on least squares support vector machine (LSSVM), and proposed a method of LSSVM-based fuzzy model control. Then we applied it in advanced casting equipment constant casting control system and mainly done the following work:
1) For the high computational complexity problem in fuzzy modeling method based on standard support vector machine, the introduction of the LSSVM with equation constraints, significantly improved the efficiency of modeling.
2) The structure of fuzzy model is identified using the LSSVM algorithm; the sparse support vectors are gotten through the pruning algorithm without changing the training parameters; the Fuzzy space is divided based on the number of support vectors. It simplifies the structure of the fuzzy model, and promotes its application.
3) The LSSVM fuzzy model is introduced into the internal model control, and used as the system's internal model. The inverse model controller is designed according to this modeling method.
4) A constant casting control system is designed. A simulation model is built after the analysis of features of the constant casting pressure control system. The simulation results show that quantitative casting surface pressure systems, internal model control method based on of LSSVM fuzzy model has certain advantages in the control precision and anti-interference capability.
引文
[1]李新雷,郝启堂,介万奇.反重力铸造装备技术的应用与发展.铸造技术,2011,32(3)：380-383.
[2]杨晶,李传大,刘云,党惊知.铝合金挤压铸造用电磁泵定量浇注技术.特种铸造及有色合金,2005,25(4)：226-228.
[3]王猛,曾建民,黄卫东.大型复杂薄壁铸件高品质高精度调压铸造技术.铸造技术,2004(5)：353-358.
[4]陈善富,刘瑞河,罗绪平.工控机在铅锭定量浇铸微机控制系统的应用.工业控制计算机,2000,13(6)：40-41。
[5]周玉川,郝启堂,李新雷等Fuzzy-PID在反重力铸造液面加压控制系统中的应用.铸造,2008,57(1)：36-39.
[6]Yang Bo, Chai Yan, Wang Yuegang. Simulation Research on the Time-Delay Property of Different-Pressure Casting's Control System.
[7]M. Davis, System Identification and Control of Counter Gravity Systems. Tennessee Technological University, REU Industrial Applications of Sensing, Modeling and Control, August2006.
[8]陈继刚,李强,王葛.铝合金轮毂低压铸造充型非线性压力条件.特种铸造及有色合金,2009,29(1)：27-29.
[9]李芳.前馈-模糊控制在低压铸造中的应用研究.信阳师范学院学报(自然科学版),2005,18(2)：234-237.
[10]徐小平,王峰,胡钢.系统辨识研究的现状.现代电子技术,2007,15(5)：112-116.
[11]Ying H., Ding Y. S., Li S. K., Shao S. H.. Comparison of necessary conditions for typical Takagi-Sugeno and Mamdani fuzzy systems as universal approximators. IEEE Trans on Systems Man and Cybernetics Part a-Systems and Humans,1999,29(5):508-514.
[12]肖建,白裔峰.模糊系统结构辨识综述.西南交通大学学报,2006,41(2)：135-142
[13]Chen Y.X., Wang J.Z.. Support Vector Learning for Fuzzy Rule-Based Classification Systems, IEEE Trans on Fuzzy Systems,2003,12(1):716-728.
[14]Mamdani E.H., Assilian S.,An experiment with in linguistic systems with a fuzzy logic controller [J]. Internatinal Journal of Man-Machine Studies,1975,7:1-13.
[15]席裕庚.预测控制[M].北京：国防工业出版社,1994.
[16]Rivals I, Personnaz. Nonlinear internal model control using neural networks:application to processes with delay and design issues. IEEE Trans on neural networks,2000,11(1):80-90.
[17]GE Baoming, WANG Xiangheng, SU Pengsheng,et al. Nonlinear internal model control for switched reluctance drives. IEEE Trans on Power Electronics,2002,17(3)379-388.
[18]Patwardhan S C, Madhavan K P. Nonlinear internal model control using quadratic prediction model. Computers and for system with measured disturbances and Chemical Engineering,1998,22(4/5):587-601.
[19]Zheng mingfang. Linear time-delay system Internal Model Control study.2006,18(1):49-51.
[20]Smola A.J., Schoelkopf B.. A tutorial on support vector regression, Statistics and Computing,2004,14(3):199-222.
[21]边肇棋,张学工著.模式识别.北京：清华大学出版,2000：284～304
[22]张学工.关于统计学习理论与支持向量机.自动化学报,2000,26(1)：32-43.
[23]杜树新,吴铁军等.模式识别中的支持向量机的方法.浙江大学学报,2003,37(5)：520-527.
[24]陈帅,朱建宁等.最小二乘支持向量机的参数优化及其应用.华东理工大学学报,2008,34(2)：278-282.
[25]刘斌,苏宏业等.一种基于最小二乘支持向量机的预测控制算法.控制与决策,2004,19(12)：1399-1402.
[26]Filippone, M.,Camastra, F., Masulli, F., Rovetta, S.. A survey of kernel and spectral methods for clustering. Pattern Recognition,2008,41(1):176-190.
[27]Yang, S. Y. Wang, M. Jiao, L. C.. Ridgelet kernel regression. Neurocomputing,2007,70(16):3046-3055.
[28]Cawley, G. C., An empirical evaluation of the fuzzy kernel perceptron. IEEE Transactions on Neural Networks,2007,18(3):935-937.
[29]Wang, Y.Q., Wang, S.Y., Lai, K.K.:A new fuzzy support vector machine to evaluate credit risk. IEEE Transactions on Fuzzy Systems13,2005:820-831.
[30]肖建,白裔峰.模糊系统结构辨识综述.西南交通大学学报,2006,41(2)：135-142.
[31]刘福才.非线性系统的模糊模型辨识及其应用.北京：国防工业出版社,2006.
[32]SUYKENS J A K, BRABANTER J D, LUKAS L, et al. Weighted least squares support vector machines:robustness and sparse approximation. Neuro computing,2002,48:85-105.
[33]Yue-hua Chen, Guang-yi Cao. LS-SVM model based nonlinear predivtive control for MCFC system. Journal of Zhejiang University SCIENCE,2007,8(5)748-754.
[34]吴青,刘三阳,杜喆.回归型模糊最小二乘支持向量机.西安电子科技大学学报(自然科学 版),2007,34(5)：773-778.
[35]Su B, Chen Z Q, Yu an Z Z. Constrained predictive control based on T-S fuzzy model for nonlinear systems. Journal of Systems Engineering andElectr onics,2007,18(1):95-100.
[36]Wei Li, Yupu Yang, Zhong Yang, Changying Zhang. Fuzzy System Identification Based on Support Vector Regression and Genetic Algorithm. Proceedings2008International Conference on Modeling, Identification and Control,2008.
[37]Byung-hwa Lee, Sang-un Kim, Jin-wook Seok and Sangchul Won. Nonlinear system identification based on support vector machine using particle swarm optimization [A]. In: SICE-ICASE International Joint Conference, Korea: IEEE Press2006.5614-5618.
[38]Kim J., Won S., New Fuzzy Inference System Using a Support Vector Machine, Proceedings of the41st IEEE Conference on Decision and Control, Las Vegas, Nevada USA,2002,2:1349-1354.
[39]Chan W.C., Cheung K.C. Haris C.J., On the Modeling of Nonlinear Dynamic Systems Using Support Vector Neural Networks, Engineering Application of Artificial Intelligence,2001,14:105-113.
[40]George Tsekouras, Haralambos Sarimveis, Evagelia Kavakli, George Bafas. A hierarchical fuzzy-clustering approach to fuzzy modeling. Fuzzy Sets and Systems,2005,15(2):245-266.
[41]Hu Q, Saha P, Rangaiah G P. Experimental evaluation of an augmented IMC for nonlinear System. Control Engineering Practice,2000,8(10):1167-1176.
[42]R. Boukezzoula, S. Galichet and L. Folloy,"Nonlinear Internal Model Control:Application of Inverse Model Based Fuzzy Control", IEEE Transactions on Fuzzy Systems,11(6):814-829,2003.(13) M.D. Brown G. Lightbody and G.W. Irwin, Nonlinear internal.
[43]Cheng zhiqiang, D. L. Kui, Youxian Sun. Furnace thermal efficiency of soft measurement and Internal Model Control. Information and Control.2004,33(1):85-88.
[44]查宏民.基于比例方向阀的气动位置控制系统控制策略的研究.2005.1.
[45]SMC(中国)有限公司.现代实用气动技术.北京：机械工业出版社,2003.
[46]曲以义.气压伺服系统.上海：上海交通大学出版社,1985：13-50.
[47]柏艳红,李小宁.比例阀摆动气缸位置伺服系统及其控制策略研究.液压与气动,2005,2：10-13.
[48]Sanville L E. A new Method of Specifying the Flow Capacity of Pneumatic Fluid Power Valves Second Fluid Power Symposium, BHRA, England, Paper D3,1971:37-47.
[59]D.麦克洛伊.流体动力控制分析与设计.机械工业出版社,1986.
[50]崔建,李佳.西门子工业网络通信指南.北京：机械工业出版社,2004.
[51]李其中,苏明,李军.S7-300PLC串行通讯及应用.机械与电子,2009(9):55-58.
[52]黄峥,古鹏.基于S7系列PLC通讯方式与设计研究.测控技术,2010,39(6):45-48.
[2]杨晶,李传大,刘云,党惊知.铝合金挤压铸造用电磁泵定量浇注技术.特种铸造及有色合金,2005,25(4)：226-228.
[3]王猛,曾建民,黄卫东.大型复杂薄壁铸件高品质高精度调压铸造技术.铸造技术,2004(5)：353-358.
[4]陈善富,刘瑞河,罗绪平.工控机在铅锭定量浇铸微机控制系统的应用.工业控制计算机,2000,13(6)：40-41。
[5]周玉川,郝启堂,李新雷等Fuzzy-PID在反重力铸造液面加压控制系统中的应用.铸造,2008,57(1)：36-39.
[6]Yang Bo, Chai Yan, Wang Yuegang. Simulation Research on the Time-Delay Property of Different-Pressure Casting's Control System.
[7]M. Davis, System Identification and Control of Counter Gravity Systems. Tennessee Technological University, REU Industrial Applications of Sensing, Modeling and Control, August2006.
[8]陈继刚,李强,王葛.铝合金轮毂低压铸造充型非线性压力条件.特种铸造及有色合金,2009,29(1)：27-29.
[9]李芳.前馈-模糊控制在低压铸造中的应用研究.信阳师范学院学报(自然科学版),2005,18(2)：234-237.
[10]徐小平,王峰,胡钢.系统辨识研究的现状.现代电子技术,2007,15(5)：112-116.
[11]Ying H., Ding Y. S., Li S. K., Shao S. H.. Comparison of necessary conditions for typical Takagi-Sugeno and Mamdani fuzzy systems as universal approximators. IEEE Trans on Systems Man and Cybernetics Part a-Systems and Humans,1999,29(5):508-514.
[12]肖建,白裔峰.模糊系统结构辨识综述.西南交通大学学报,2006,41(2)：135-142
[13]Chen Y.X., Wang J.Z.. Support Vector Learning for Fuzzy Rule-Based Classification Systems, IEEE Trans on Fuzzy Systems,2003,12(1):716-728.
[14]Mamdani E.H., Assilian S.,An experiment with in linguistic systems with a fuzzy logic controller [J]. Internatinal Journal of Man-Machine Studies,1975,7:1-13.
[15]席裕庚.预测控制[M].北京：国防工业出版社,1994.
[16]Rivals I, Personnaz. Nonlinear internal model control using neural networks:application to processes with delay and design issues. IEEE Trans on neural networks,2000,11(1):80-90.
[17]GE Baoming, WANG Xiangheng, SU Pengsheng,et al. Nonlinear internal model control for switched reluctance drives. IEEE Trans on Power Electronics,2002,17(3)379-388.
[18]Patwardhan S C, Madhavan K P. Nonlinear internal model control using quadratic prediction model. Computers and for system with measured disturbances and Chemical Engineering,1998,22(4/5):587-601.
[19]Zheng mingfang. Linear time-delay system Internal Model Control study.2006,18(1):49-51.
[20]Smola A.J., Schoelkopf B.. A tutorial on support vector regression, Statistics and Computing,2004,14(3):199-222.
[21]边肇棋,张学工著.模式识别.北京：清华大学出版,2000：284～304
[22]张学工.关于统计学习理论与支持向量机.自动化学报,2000,26(1)：32-43.
[23]杜树新,吴铁军等.模式识别中的支持向量机的方法.浙江大学学报,2003,37(5)：520-527.
[24]陈帅,朱建宁等.最小二乘支持向量机的参数优化及其应用.华东理工大学学报,2008,34(2)：278-282.
[25]刘斌,苏宏业等.一种基于最小二乘支持向量机的预测控制算法.控制与决策,2004,19(12)：1399-1402.
[26]Filippone, M.,Camastra, F., Masulli, F., Rovetta, S.. A survey of kernel and spectral methods for clustering. Pattern Recognition,2008,41(1):176-190.
[27]Yang, S. Y. Wang, M. Jiao, L. C.. Ridgelet kernel regression. Neurocomputing,2007,70(16):3046-3055.
[28]Cawley, G. C., An empirical evaluation of the fuzzy kernel perceptron. IEEE Transactions on Neural Networks,2007,18(3):935-937.
[29]Wang, Y.Q., Wang, S.Y., Lai, K.K.:A new fuzzy support vector machine to evaluate credit risk. IEEE Transactions on Fuzzy Systems13,2005:820-831.
[30]肖建,白裔峰.模糊系统结构辨识综述.西南交通大学学报,2006,41(2)：135-142.
[31]刘福才.非线性系统的模糊模型辨识及其应用.北京：国防工业出版社,2006.
[32]SUYKENS J A K, BRABANTER J D, LUKAS L, et al. Weighted least squares support vector machines:robustness and sparse approximation. Neuro computing,2002,48:85-105.
[33]Yue-hua Chen, Guang-yi Cao. LS-SVM model based nonlinear predivtive control for MCFC system. Journal of Zhejiang University SCIENCE,2007,8(5)748-754.
[34]吴青,刘三阳,杜喆.回归型模糊最小二乘支持向量机.西安电子科技大学学报(自然科学 版),2007,34(5)：773-778.
[35]Su B, Chen Z Q, Yu an Z Z. Constrained predictive control based on T-S fuzzy model for nonlinear systems. Journal of Systems Engineering andElectr onics,2007,18(1):95-100.
[36]Wei Li, Yupu Yang, Zhong Yang, Changying Zhang. Fuzzy System Identification Based on Support Vector Regression and Genetic Algorithm. Proceedings2008International Conference on Modeling, Identification and Control,2008.
[37]Byung-hwa Lee, Sang-un Kim, Jin-wook Seok and Sangchul Won. Nonlinear system identification based on support vector machine using particle swarm optimization [A]. In: SICE-ICASE International Joint Conference, Korea: IEEE Press2006.5614-5618.
[38]Kim J., Won S., New Fuzzy Inference System Using a Support Vector Machine, Proceedings of the41st IEEE Conference on Decision and Control, Las Vegas, Nevada USA,2002,2:1349-1354.
[39]Chan W.C., Cheung K.C. Haris C.J., On the Modeling of Nonlinear Dynamic Systems Using Support Vector Neural Networks, Engineering Application of Artificial Intelligence,2001,14:105-113.
[40]George Tsekouras, Haralambos Sarimveis, Evagelia Kavakli, George Bafas. A hierarchical fuzzy-clustering approach to fuzzy modeling. Fuzzy Sets and Systems,2005,15(2):245-266.
[41]Hu Q, Saha P, Rangaiah G P. Experimental evaluation of an augmented IMC for nonlinear System. Control Engineering Practice,2000,8(10):1167-1176.
[42]R. Boukezzoula, S. Galichet and L. Folloy,"Nonlinear Internal Model Control:Application of Inverse Model Based Fuzzy Control", IEEE Transactions on Fuzzy Systems,11(6):814-829,2003.(13) M.D. Brown G. Lightbody and G.W. Irwin, Nonlinear internal.
[43]Cheng zhiqiang, D. L. Kui, Youxian Sun. Furnace thermal efficiency of soft measurement and Internal Model Control. Information and Control.2004,33(1):85-88.
[44]查宏民.基于比例方向阀的气动位置控制系统控制策略的研究.2005.1.
[45]SMC(中国)有限公司.现代实用气动技术.北京：机械工业出版社,2003.
[46]曲以义.气压伺服系统.上海：上海交通大学出版社,1985：13-50.
[47]柏艳红,李小宁.比例阀摆动气缸位置伺服系统及其控制策略研究.液压与气动,2005,2：10-13.
[48]Sanville L E. A new Method of Specifying the Flow Capacity of Pneumatic Fluid Power Valves Second Fluid Power Symposium, BHRA, England, Paper D3,1971:37-47.
[59]D.麦克洛伊.流体动力控制分析与设计.机械工业出版社,1986.
[50]崔建,李佳.西门子工业网络通信指南.北京：机械工业出版社,2004.
[51]李其中,苏明,李军.S7-300PLC串行通讯及应用.机械与电子,2009(9):55-58.
[52]黄峥,古鹏.基于S7系列PLC通讯方式与设计研究.测控技术,2010,39(6):45-48.